When 1 mole of gas is heated at constant volume, the temperature rises form $273 \mathrm{~K}$ to $546…

When 1 mole of gas is heated at constant volume, the temperature rises form $273 \mathrm{~K}$ to $546 \mathrm{~K}$. If heat supplied to the gas is $\mathrm{xJ}$, then find the correct statement from following.
  1. $\mathrm{Q}=\Delta \mathrm{U}=\mathrm{x}, \mathrm{W}=0$
  2. $\mathrm{Q}=\mathrm{W}=\mathrm{x} J, \Delta \mathrm{V}=0$
  3. $\Delta \mathrm{V}=0, \mathrm{Q}=\mathrm{W}=-\mathrm{x} J$
  4. $\mathrm{Q}=-\mathrm{W}=\mathrm{x} J, \Delta \mathrm{V}=0$

Solution

$\mathrm{W}=- \text { Pext. } \Delta \mathrm{V}$ Due to constant volume $\Delta \mathrm{V}=0, \mathrm{~W}=0$ $q=x J$ First law of thermodynamics, $\begin{aligned} & \Delta \mathrm{U}=\mathrm{q}+\mathrm{w} \\ & \Delta \mathrm{U}=\mathrm{xJ}=\mathrm{q} \end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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